You can copy and paste the effect to a new layer without forcing a reanalysis if the source pixel dimensions are the same. This may work fine for steroscopic pairs, in which the cameras are moving identically. I would guess that the subspace warp method wouldn't work well, since it's doing per-pixel distortions, but the Position, Scale, and Rotate method should work.

We didn't intend for the effect to be used this way, but I also can't see why it shouldn't work in this limited scenario. Let us know how it works.

Here's what one of the software engineers who worked on this feature said when I asked him to take a look at this thread:

"I wouldn't rule out Subspace Warp in this case, mainly because the warp itself is has no high spatial frequencies, so I wouldn't expect exact pixel alignment to be that critical. That said, I wouldn't be surprised if doing any method on both eyes in this way gives you a headache."

Aside from all the technicalities re the Warp Stabilizer, your recorded footage never is 100% congruent in the first place, so even a conventional stabilization would not be transferrable without some intervention. Obviously for that reason companies sell specialised stereo 3D tools/ plug-ins...

Stabilization is now over. I used the perspective option, which I guess is a corner pin, and it worked very well.

The 2 cameras were mounted on the same rail, side by side, at the top front of a big houseboat, cruising on the Seine, thru Paris.

The jitter I wanted to remove was mainly boat pitch (Z rotation) and driving (X pan). As suspected, pitch and pan were really equivalent from one camera to the other, and copying/pasting warp stabilizer once analyse was done, gave such straightforward results that I didn't try other methods.

Thank you everyone for your great help, and sincere congratulations to warp stabilizer dev team!